Question: Solve for $t$, $ -\dfrac{9}{3t} = \dfrac{5}{3t} + \dfrac{3t + 8}{15t} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $3t$ $3t$ and $15t$ The common denominator is $15t$ To get $15t$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ -\dfrac{9}{3t} \times \dfrac{5}{5} = -\dfrac{45}{15t} $ To get $15t$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ \dfrac{5}{3t} \times \dfrac{5}{5} = \dfrac{25}{15t} $ The denominator of the third term is already $15t$ , so we don't need to change it. This give us: $ -\dfrac{45}{15t} = \dfrac{25}{15t} + \dfrac{3t + 8}{15t} $ If we multiply both sides of the equation by $15t$ , we get: $ -45 = 25 + 3t + 8$ $ -45 = 3t + 33$ $ -78 = 3t $ $ t = -26$